Integral graph

In the mathematical field of graph theory, an integral graph is a graph whose spectrum consists entirely of integers. In other words, a graph is an integral graph if all of the roots of its characteristic polynomial are integers.

The notion was introduced in 1974 by Harary and Schwenk.

Examples

• The complete graph K_n is integral for all n.
• The edgeless graph ${\bar {K}}_{n}$ is integral for all n.
• Among the cubic symmetric graphs the utility graph, the Petersen graph, the Nauru graph and the Desargues graph are integral.
• The Higman–Sims graph, the Hall–Janko graph, the Clebsch graph, the Hoffman–Singleton graph, the Shrikhande graph and the Hoffman graph are integral.